Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-Form Approach

Yacine Ait-Sahalia

No 222, NBER Technical Working Papers from National Bureau of Economic Research, Inc

Abstract: When a continuous-time diffusion is observed only at discrete dates, not necessarily close together, the likelihood function of the observations is in most cases not explicitly computable. Researchers have relied on simulations of sample paths in between the observations points, or numerical solutions of partial differential equations, to obtain estimates of the function to be maximized. By contrast, we construct a sequence of fully explicit functions which we show converge under very general conditions, including non-ergodicity, to the true (but unknown) likelihood function of the discretely-sampled diffusion. We document that the rate of convergence of the sequence is extremely fast for a number of examples relevant in finance. We then show that maximizing the sequence instead of the true function results in an estimator which converges to the true maximum-likelihood estimator and shares its asymptotic properties of consistency, asymptotic normality and efficiency. Applications to the valuation of derivative securities are also discussed.

JEL-codes: C13 G12 (search for similar items in EconPapers)
Date: 1998-02
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (13)

Published as "Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-Form Approach", Econometrica, Vol. 70, pp. 223-262, (2002).

Downloads: (external link)
http://www.nber.org/papers/t0222.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:nbr:nberte:0222

Ordering information: This working paper can be ordered from
http://www.nber.org/papers/t0222

Access Statistics for this paper

More papers in NBER Technical Working Papers from National Bureau of Economic Research, Inc National Bureau of Economic Research, 1050 Massachusetts Avenue Cambridge, MA 02138, U.S.A.. Contact information at EDIRC.
Bibliographic data for series maintained by ().